Most Popular Books by Kathleen Ryan

This dynamic full-colour text actively engages students in their exploration of Canadian law and its social, political, and global ramifications. Canadian and International Law connects the historical roots of law to issues in contemporary society. Developed and tested by highly experienced teachers, subject specialists, and students for maximum classroom applicability. This text is sufficiently rigorous for university prep, yet has been designed to meet the language and interests of grade 12 students.

Movement has been made in recent times to generalize the study of degree sequences to k-edge-colored graphs and doing so requires the notion of a degree vector. The degree vector of a vertex v in a k-edge-colored graph is a (kx1) column vector in which entry i indicates the number of edges of color i incident to v. Consider the following question which we refer to as the k-Edge-Coloring Problem. Given a set of column vectors C and a graph family F, when does there exist some k-edge-colored graph in F whose set of degree vectors is C? This question is NP-Complete in general but certain graph families yield tractable results. In this document, I present results on the k-Edge-Coloring Problem and the related Factor Problem for the following families of interest: unicyclic graphs , disjoint unions of paths (DUPs), disjoint union of cycles (DUCs), grids, and 2-trees. Specifically, in Chapter 1, I characterize the degree vector sequences of k-edge-colored unicylcic graphs, and in Chapter 2, I characterize degree sequences of factors of fixed DUPs, fixed DUCs, and fixed graphs with maximum degree at most 2. In Chapter 3, I characterize degree vector sequences of 2-edge-colored fixed DUPs and fixed DUCs, and in doing so, I show that one restricted case for each is NP-hard. Finally, I characterize degree sequences of grid factors in a subset of cases in Chapter 4 and degree sequences of partial 2-trees in Chapter 5.